Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas. >

Particle-in-Cell Charged Particle Simulations, plus Monte Carlo Collisions with Neutral Atoms, PIC-MCC

https://zenodo.org/record/1253854/files/article.pdf

A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges

Fluid, particle-in-cell and hybrid models are the numerical simulation techniques commonly used for simulating low-temperature plasma discharges. Despite the complexity of plasma systems and the challenges in describing and modelling them, well-organized simulation methods can provide physical information often difficult to obtain from experiments. Simulation results can also be used to identify research guidelines, find optimum operating conditions or propose novel designs for performance improvements. In this paper, we present an overview of the principles, strengths and limitations of the three simulation models, including a brief history and the recent status of their development. The three modelling techniques are benchmarked by comparing simulation results in different plasma systems (plasma display panels, capacitively coupled plasmas and inductively coupled plasmas) with experimentally measured data. In addition, different aspects of the electron and ion kinetics in these systems are discussed based upon simulation results.

https://www3.nd.edu/~sst/teaching/AME60637/reading/2005_JPDAP_Kim_Iza_Yang_particle_fluid_modeling.pdf

Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects

Negative hydrogen/deuterium ions can be formed by processes occurring in the plasma volume and on surfaces facing the plasma. The principal mechanisms leading to the formation of these negative ions are dissociative electron attachment to ro-vibrationally excited hydrogen/deuterium molecules when the reaction takes place in the plasma volume, and the direct electron transfer from the low work function metal surface to the hydrogen/deuterium atoms when formation occurs on the surface. The existing theoretical models and reported experimental results on these two mechanisms are summarized. Performance of the negative hydrogen/deuterium ion sources that emerged from studies of these mechanisms is reviewed. Contemporary negative ion sources do not have negative ion production electrodes of original surface type sources but are operated with caesium with their structures nearly identical to volume production type sources. Reasons for enhanced negative ion current due to caesium addition to these sources are discussed.

Negative hydrogen ion production mechanisms

The heating of electrons by time-varying fields is fundamental to the operation of radio frequency (RF) and microwave discharges. Ohmic heating, in which the phase of the electron oscillation motion in the field is randomized locally by interparticle collisions, can dominate at high pressures. Phase randomization can also occur due to electron thermal motion in spatially inhomogeneous RF fields, even in the absence of collisions, leading to collisionless or stochastic heating, which can dominate at low pressures, Generally, electrons are heated collisionlessly by repeated interaction with fields that are localized within a sheath, skin depth layer, or resonance layer inside the discharge. This suggests the simple heating model of a ball bouncing elastically back and forth between a fixed and an oscillating wall. Such a model was proposed originally by Fermi to explain the origin of cosmic rays. In this review, Fermi acceleration is used as a paradigm to describe collisionless heating and phase randomization in capacitive, inductive, and electron cyclotron resonance (ECR) discharges. Mapping models for Fermi acceleration are introduced, and the Fokker-Planck description of the heating and the effects of phase correlations are described. The collisionless heating rates are determined in capacitive and inductive discharges and compared with self-consistent (kinetic) calculations where available. Experimental measurements and computer simulations are reviewed and compared to theoretical calculations. Recent measurements and calculations of nonlocal heating effects, such as negative electron power absorption, are described, Incomplete phase randomization and adiabatic barriers are shown to modify the heating in low pressure ECR discharges.

From Fermi acceleration to collisionless discharge heating

A retarding field energy analyzer designed to measure ion energy distributions impacting a radio-frequency biased electrode in a plasma discharge is examined. The analyzer is compact so that the need for differential pumping is avoided. The analyzer is designed to sit on the electrode surface, in place of the substrate, and the signal cables are fed out through the reactor side port. This prevents the need for modifications to the rf electrode—as is normally the case for analyzers built into such electrodes. The capabilities of the analyzer are demonstrated through experiments with various electrode bias conditions in an inductively coupled plasma reactor. The electrode is initially grounded and the measured distributions are validated with the Langmuir probe measurements of the plasma potential. Ion energy distributions are then given for various rf bias voltage levels, discharge pressures, rf bias frequencies—500kHzto30MHz, and rf bias waveforms—sinusoidal, square, and dual frequency.

Retarding field analyzer for ion energy distribution measurements at a radio-frequency biased electrode

We have determined the electron energy distribution function (EEDF) in a low pressure nitrogen rf discharge both experimentally and using a computer simulation. The EEDFs show unusual structures, which can be interpreted in terms of a sheath-oscillation electron heating mechanism. However, the simulation shows that contrary to the conventional model, the electrons are heated in part by retreating sheaths. We present an analytical treatment of this phenomenon.

Anomalous sheath heating in a low pressure rf discharge in nitrogen.

We show that a recently proposed pressure model of collisionless heating in capacitive rf discharges predicts that a small magnetic field ({approximately}10 G) applied transverse to the electric field will induce a heating mode transition from a pressure-heating dominated state to an Ohmic-heating dominated state. This prediction is confirmed by kinetic simulations and experiments. {copyright} {ital 1996 The American Physical Society.}

Heating mode transition induced by a magnetic field in a capacitive rf discharge.

A commercial retarding field analyzer is used to measure the time-averaged ion energy distributions of impacting ions at the powered electrode in a 13.56 MHz driven, capacitively coupled, parallel plate discharge operated at low pressure. The study is carried out in argon discharges at 10 mTorr where the sheaths are assumed to be collisionless. The analyzer is mounted flush with the powered electrode surface where the impacting ion and electron energy distributions are measured for a range of discharge powers. A circuit model of the discharge, in combination with analytical solutions for the ion energy distribution in radio-frequency sheaths, is used to calculate other important plasma parameters from the measured energy distributions. Radio-frequency compensated Langmuir probe measurements provide a comparison with the retarding field analyzer data. The time-resolved capability of the retarding field analyzer is also demonstrated in a separate pulsed dc magnetron reactor. The analyzer is mounted on the floating substrate holder and ion energy distributions of the impinging ions on a growing film, with 100 ns time resolution, are measured through a pulse period of applied magnetron power, which are crucial for the control of the microstructure and properties of the deposited films.

/pdf/ion-energy-distribution-measurements-in-rf-and-pulsed-dc-1br5v4m4us.pdf

Ion energy distribution measurements in rf and pulsed dc plasma discharges

A comparison is made between plasma parameters measured with a retarding field energy analyzer (RFEA), mounted at a grounded electrode in an inductive discharge, and a Langmuir probe located in bulk plasma close to the analyzer. Good agreement between measured plasma parameters is obtained for argon gas pressure in the range 2?10?mTorr. Parameters compared include time averaged plasma potential, the tail of the electron energy distribution function (EEDF), the electron temperature and the ion flux. This highlights the versatility of the RFEA for determining plasma parameters adjacent to the surface where probe measurements are not easily made. Combination of the probe and energy analyzer has enabled the measurement of the EEDF to a higher energy than otherwise possible.

https://iopscience.iop.org/article/10.1088/0963-0252/17/3/035026/pdf

M. B. Hopkins

Papers

Retarding field analyzer for ion energy distribution measurements at a radio-frequency biased electrode

Anomalous sheath heating in a low pressure rf discharge in nitrogen.

Heating mode transition induced by a magnetic field in a capacitive rf discharge.

Ion energy distribution measurements in rf and pulsed dc plasma discharges

Comparison of plasma parameters determined with a Langmuir probe and with a retarding field energy analyzer